Non-line-of-sight Node Localization based on Semi-Definite Programming in Wireless Sensor Networks

An unknown-position sensor can be localized if there are three or more anchors making time-of-arrival (TOA) measurements of a signal from it. However, the location errors can be very large due to the fact that some of the measurements are from non-line-of-sight (NLOS) paths. In this paper, we propose a semi-definite programming (SDP) based node localization algorithm in NLOS environment for ultra-wideband (UWB) wireless sensor networks. The positions of sensors can be estimated using the distance estimates from location-aware anchors as well as other sensors. However, in the absence of LOS paths, e.g., in indoor networks, the NLOS range estimates can be significantly biased. As a result, the NLOS error can remarkably decrease the location accuracy. And it is not easy to efficiently distinguish LOS from NLOS measurements. In this paper, an algorithm is proposed that achieves high location accuracy without the need of identifying NLOS and LOS measurement.Comment: submitted to IEEE ICC'1

On geometric upper bounds for positioning algorithms in wireless sensor networks

This paper studies the possibility of upper bounding the position error for range-based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances between sensor nodes have positive errors, e.g., in non-line-of-sight (NLOS) conditions, the target node is confined to a closed bounded convex set (a feasible set) which can be derived from the measurements. Then, we formulate two classes of geometric upper bounds with respect to the feasible set. If an estimate is available, either feasible or infeasible, the position error can be upper bounded as the maximum distance between the estimate and any point in the feasible set (the first bound). Alternatively, if an estimate given by a positioning algorithm is always feasible, the maximum length of the feasible set is an upper bound on position error (the second bound). These bounds are formulated as nonconvex optimization problems. To progress, we relax the nonconvex problems and obtain convex problems, which can be efficiently solved. Simulation results show that the proposed bounds are reasonably tight in many situations, especially for NLOS conditions

Collaborative Sensor Network Localization: Algorithms and Practical Issues

Emerging communication network applications including fifth-generation (5G) cellular and the Internet-of-Things (IoT) will almost certainly require location information at as many network nodes as possible. Given the energy requirements and lack of indoor coverage of Global Positioning System (GPS), collaborative localization appears to be a powerful tool for such networks. In this paper, we survey the state of the art in collaborative localization with an eye toward 5G cellular and IoT applications. In particular, we discuss theoretical limits, algorithms, and practical challenges associated with collaborative localization based on range-based as well as range-angle-based techniques

Localization Of Sensors In Presence Of Fading And Mobility

The objective of this dissertation is to estimate the location of a sensor through analysis of signal strengths of messages received from a collection of mobile anchors. In particular, a sensor node determines its location from distance measurements to mobile anchors of known locations. We take into account the uncertainty and fluctuation of the RSS as a result of fading and take into account the decay of the RSS which is proportional to the transmitter-receiver distance power raised to the PLE. The objective is to characterize the channel in order to derive accurate distance estimates from RSS measurements and then utilize the distance estimates in locating the sensors. To characterize the channel, two techniques are presented for the mobile anchors to periodically estimate the channel\u27s PLE and fading parameter. Both techniques estimate the PLE by solving an equation via successive approximations. The formula in the first is stated directly from MLE analysis whereas in the second is derived from a simple probability analysis. Then two distance estimates are proposed, one based on a derived formula and the other based on the MLE analysis. Then a location technique is proposed where two anchors are sufficient to uniquely locate a sensor. That is, the sensor narrows down its possible locations to two when collects RSS measurements transmitted by a mobile anchor, then uniquely determines its location when given a distance to the second anchor. Analysis shows the PLE has no effect on the accuracy of the channel characterization, the normalized error in the distance estimation is invariant to the estimated distance, and accurate location estimates can be achieved from a moderate sample of RSS measurements

Localization and cooperative communication methods for cognitive radio

We study localization of nearby nodes and cooperative communication for cognitive radios. Cognitive radios sensing their environment to estimate the channel gain between nodes can cooperate and adapt their transmission power to maximize the capacity of the communication between two nodes. We study the end-to-end capacity of a cooperative relaying scheme using orthogonal frequency-division modulation (OFDM) modulation, under power constraints for both the base station and the relay station. The relay uses amplify-and-forward and decodeand-forward cooperative relaying techniques to retransmit messages on a subset of the available subcarriers. The power used in the base station and the relay station transmitters is allocated to maximize the overall system capacity. The subcarrier selection and power allocation are obtained based on convex optimization formulations and an iterative algorithm. Additionally, decode-and-forward relaying schemes are allowed to pair source and relayed subcarriers to increase further the capacity of the system. The proposed techniques outperforms non-selective relaying schemes over a range of relay power budgets. Cognitive radios can be used for opportunistic access of the radio spectrum by detecting spectrum holes left unused by licensed primary users. We introduce a spectrum holes detection approach, which combines blind modulation classification, angle of arrival estimation and number of sources detection. We perform eigenspace analysis to determine the number of sources, and estimate their angles of arrival (AOA). In addition, we classify detected sources as primary or secondary users with their distinct second-orde one-conjugate cyclostationarity features. Extensive simulations carried out indicate that the proposed system identifies and locates individual sources correctly, even at -4 dB signal-to-noise ratios (SNR). In environments with a high density of scatterers, several wireless channels experience non-line-of-sight (NLOS) condition, increasing the localization error, even when the AOA estimate is accurate. We present a real-time localization solver (RTLS) for time-of-arrival (TOA) estimates using ray-tracing methods on the map of the geometry of walls and compare its performance with classical TOA trilateration localization methods. Extensive simulations and field trials for indoor environments show that our method increases the coverage area from 1.9% of the floor to 82.3 % and the accuracy by a 10-fold factor when compared with trilateration. We implemented our ray tracing model in C++ using the CGAL computational geometry algorithm library. We illustrate the real-time property of our RTLS that performs most ray tracing tasks in a preprocessing phase with time and space complexity analyses and profiling of our software

Algorithms for Positioning with Nonlinear Measurement Models and Heavy-tailed and Asymmetric Distributed Additive Noise

Determining the unknown position of a user equipment using measurements obtained from transmitters with known locations generally results in a nonlinear measurement function. The measurement errors can have a heavy-tailed and/ or skewed distribution, and the likelihood function can be multimodal.A positioning problem with a nonlinear measurement function is often solved by a nonlinear least squares (NLS) method or, when filtering is desired, by an extended Kalman filter (EKF). However, these methods are unable to capture multiple peaks of the likelihood function and do not address heavy-tailedness or skewness. Approximating the likelihood by a Gaussian mixture (GM) and using a GM filter (GMF) solves the problem. The drawback is that the approximation requires a large number of components in the GM for a precise approximation, which makes it unsuitable for real-time positioning on small mobile devices.This thesis studies a generalised version of Gaussian mixtures, which is called GGM, to capture multiple peaks. It relaxes the GM’s restriction to non-negative component weights. The analysis shows that the GGM allows a significant reduction of the number of required Gaussian components when applied for approximating the measurement likelihood of a transmitter with an isotropic antenna, compared with the GM. Therefore, the GGM facilitates real-time positioning in small mobile devices. In tests for a cellular telephone network and for an ultra-wideband network the GGM and its filter provide significantly better positioning accuracy than the NLS and the EKF.For positioning with nonlinear measurement models, and heavytailed and skewed distributed measurement errors, an Expectation Maximisation (EM) algorithm is studied. The EM algorithm is compared with a standard NLS algorithm in simulations and tests with realistic emulated data from a long term evolution network. The EM algorithm is more robust to measurement outliers. If the errors in training and positioning data are similar distributed, then the EM algorithm yields significantly better position estimates than the NLS method. The improvement in accuracy and precision comes at the cost of moderately higher computational demand and higher vulnerability to changing patterns in the error distribution (of training and positioning data). This vulnerability is caused by the fact that the skew-t distribution (used in EM) has 4 parameters while the normal distribution (used in NLS) has only 2. Hence the skew-t yields a closer fit than the normal distribution of the pattern in the training data. However, on the downside if patterns in training and positioning data vary than the skew-t fit is not necessarily a better fit than the normal fit, which weakens the EM algorithm’s positioning accuracy and precision. This concept of reduced generalisability due to overfitting is a basic rule of machine learning.This thesis additionally shows how parameters of heavy-tailed and skewed error distributions can be fitted to training data. It furthermore gives an overview on other parametric methods for solving the positioning method, how training data is handled and summarised for them, how positioning is done by them, and how they compare with nonparametric methods. These methods are analysed by extensive tests in a wireless area network, which shows the strength and weaknesses of each method